BiClustering

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Bi-Clustering

• COMP 790-90 Seminar
• Spring 2009

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Data Mining Clustering
K-means clustering minimizes
Where
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Clustering by Pattern Similarity (p-Clustering)

• The micro-array raw data shows 3 genes and
  their values in a multi-dimensional space
• Parallel Coordinates Plots
• Difficult to find their patterns
• non-traditional clustering

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Clusters Are Clear After Projection
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Motivation

• E-Commerce collaborative filtering

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Motivation
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Motivation
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Motivation
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Motivation

• DNA microarray analysis

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Motivation
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Motivation

• Strong coherence exhibits by the selected objects
  on the selected attributes.
• They are not necessarily close to each other but
  rather bear a constant shift.
• Object/attribute bias
• bi-cluster

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Challenges

• The set of objects and the set of attributes are
  usually unknown.
• Different objects/attributes may possess
  different biases and such biases
• may be local to the set of selected
  objects/attributes
• are usually unknown in advance
• May have many unspecified entries

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Previous Work

• Subspace clustering
• Identifying a set of objects and a set of
  attributes such that the set of objects are
  physically close to each other on the subspace
  formed by the set of attributes.
• Collaborative filtering Pearson R
• Only considers global offset of each
  object/attribute.

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bi-cluster

• Consists of a (sub)set of objects and a (sub)set
  of attributes
• Corresponds to a submatrix
• Occupancy threshold ?
• Each object/attribute has to be filled by a
  certain percentage.
• Volume number of specified entries in the
  submatrix
• Base average value of each object/attribute (in
  the bi-cluster)

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bi-cluster
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bi-cluster

• Perfect ?-cluster
• Imperfect ?-cluster
• Residue

dij
diJ
dIJ
dIj
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bi-cluster

• The smaller the average residue, the stronger the
  coherence.
• Objective identify ?-clusters with residue
  smaller than a given threshold

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Cheng-Church Algorithm

• Find one bi-cluster.
• Replace the data in the first bi-cluster with
  random data
• Find the second bi-cluster, and go on.
• The quality of the bi-cluster degrades (smaller
  volume, higher residue) due to the insertion of
  random data.

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The FLOC algorithm
Generating initial clusters
Determine the best action for each row and each
column
Perform the best action of each row and column
sequentially
Y
Improved?
N
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The FLOC algorithm

• Action the change of membership of a row(or
  column) with respect to a cluster

column
M4
1
2
3
4
row
3
4
2
2
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MN actions are Performed at each iteration
1
3
3
2
2
N3
4
2
0
4
3
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The FLOC algorithm

• Gain of an action the residue reduction incurred
  by performing the action
• Order of action
• Fixed order
• Random order
• Weighted random order
• Complexity O((MN)MNkp)

?
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The FLOC algorithm

• Additional features
• Maximum allowed overlap among clusters
• Minimum coverage of clusters
• Minimum volume of each cluster
• Can be enforced by temporarily blocking certain
  action during the mining process if such action
  would violate some constraint.

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Performance

• Microarray data 2884 genes, 17 conditions
• 100 bi-clusters with smallest residue were
  returned.
• Average residue 10.34
• The average residue of clusters found via the
  state of the art method in computational biology
  field is 12.54
• The average volume is 25 bigger
• The response time is an order of magnitude faster

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Conclusion Remark

• The model of bi-cluster is proposed to capture
  coherent objects with incomplete data set.
• base
• residue
• Many additional features can be accommodated
  (nearly for free).